Equality of Segments on the Axis of a Parabola

This GeoGebra example demonstrates a geometric property where certain segments on the axis of a parabola are equal in length. The core mathematical concepts involve the focus, directrix, tangents, axis of symmetry, and the associated parallelogram and incircle. The construction uses GeoGebra commands such as Intersect, Point, Mirror, Tangent, OrthogonalLine, Line, Focus, Segment, and Angle, creating objects like the parabola p, circle c, text labels, points K, L, G, E, H, F, lines f, g, h, i, k, and angles α and β. By leveraging symmetry and perpendicularity, the equality of segments (e.g., distances from the focus to certain intersection points) is verified. This is suitable for high school or college analytic geometry courses, helping students explore parabolic symmetry and geometric construction techniques, and can serve as an interactive investigation tool.